Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized TMDPDFs at Physical Quark Masses

We present the first lattice QCD calculations of the isovector helicity transverse momentum-dependent parton distribution function (TMDPDF) and the flavor-dependent unpolarized TMDPDFs for up and down quarks in the proton. Our computations utilize domain-wall fermion discretization with physical quark masses. Employing Coulomb-gauge-fixed bilocal quark correlation functions within the large-momentum effective theory framework, we access nonperturbative transverse quark separations bT up to approximately 1~fm, corresponding to low transverse momentum scales. We present renormalization and factorization scale-independent ratios of these TMDPDFs as functions of bT and longitudinal momentum fraction x, allowing direct comparisons with phenomenological parameterizations from global experimental fits. Our results demonstrate remarkably similar bT dependence between helicity and unpolarized TMDPDFs at moderate x, in agreement with phenomenology. In contrast to certain phenomenological models, we observe mild flavor dependence in the bT distributions at moderate values of x.